Deceleration and heating constrained footprint of shuttle vehicles

With increasing frequency in shuttle operation, it is of interest to have more than one or two landing fields within the boundary of the reachable area of the reentry vehicle. This boundary, called the footprint, depends on the aerodynamic characteristics of the vehicle and is severely restricted by the deceleration and heating constraints imposed upon the atmospheric reentry trajectory. This paper gives a general assessment of the footprint as a function of various deceleration and heating constraints. The difficulties in the computation of the three-dimensional reentry trajectories with optimal modulation in both the angle-of-attack and the bank angle are alleviated by the following devices: (a) nondimensionalizing of the equations of motion and use of the density as the altitude variable; (b) use of the classical integrals of the motion; (c) transformation of the adjoint variables into physical variables; and (d) spherical rotation of the coordinates.